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Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$

by Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier

Submission summary

As Contributors: Grégoire Misguich
Arxiv Link: (pdf)
Date submitted: 2020-11-17 11:00
Submitted by: Misguich, Grégoire
Submitted to: SciPost Physics
Academic field: Physics
  • Mathematical Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group $U_q(\widehat{sl}_n)$. Compared with the conventional $(n-1)$-color BBS, it enjoys a remarkable simplification that scattering of solitons is totally diagonal. We also introduce a randomized cBBS and study its non-equilibrium behavior by thermodynamic Bethe ansatz and generalized hydrodynamics. Excellent agreement is demonstrated between theoretical predictions and numerical simulation on the density plateaux generated from domain wall initial conditions including their diffusive broadening.

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Submission 2011.08052v1 on 17 November 2020

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